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Sunday, July 31, 2016

Clever Hardy


"Hardy used the Riemann hypothesis as insurance when crossing the North sea after his summer visit to his friend Harald Bohr in Denmark. Before leaving port he would send his friend a postcard with the claim that he had just proved the Riemann hypothesis. It was a clever each way bet. If the boat sank he would have the posthumous honour of solving the great problem. On the other hand, if God did exist he would not let an atheist like Hardy have that honour and would therefore prevent the boat from sinking."

-- Tony Crilly

[p.s... with the political conventions over, blogging here and at MathTango, will likely return to normal in the coming week]


Monday, July 25, 2016

Three to Expect a Lot From


An interesting piece on 3 leading, young European mathematicians,  Peter Scholze,  James Maynard, and Sara Zahedi, who are "surprisingly young -- and very down-to-earth(h/t to Egan Chernoff for this one):

http://www.dw.com/en/dont-call-me-a-prodigy-the-rising-stars-of-european-mathematics/a-19421389


Sunday, July 24, 2016

"mathematics is permanent"


This  week's Sunday reflection from Freeman Dyson:
"...it’s the beauty of mathematics, as opposed to physics, that it’s forever. I published my selected papers recently in one volume, and I found out that when you publish your selected papers most of the physics is ephemeral, that you don’t want to publish stuff that was written 10 or 20 years earlier, but the mathematics is permanent. So essentially everything I’ve ever published in mathematics is there, whereas only about a quarter of what I published on physics was worth preserving."

Wednesday, July 20, 2016

"an extreme sensitivity to numbers"



Am largely taking vacation from blogging for a couple of weeks (’til political conventions are over), and will again skip Friday potpourri over at MathTango, but put up an occasional post here (and still be on Twitter) -- between the two blogs I've averaged over 5 posts per week for the last 6 years so won’t feel too guilty taking a vacation ;-)
Anyway, passing along this interesting recent piece from the Christian Science Monitor on a supposed real life “Good Will Hunting” Chinese migrant (Yu Jianchun) using a creative/imaginative approach to solve a long-standing problem involving “Carmichael numbers” :
…alternatively, this coverage from the Washington Post:
With all the reporting on Ramanujan in recent months (including in these articles), Yu's story sounds a bit familiar. According to one professor, “All he has is an instinct and an extreme sensitivity to numbers.” And Yu himself says, “I made my discoveries through intuition.”

I love this almost inexplicable notion of math prodigies and savants possessing a “sensitivity to numbers,” whatever that means, and connecting to mathematics more through intuition than pure deduction. In some way it harks back to the Platonist/non-Platonist divide in mathematics. Are such gifted individuals intuitively in touch with some Platonic realm of math that exists apart from humans, and that most of us lack direct access to, or are they merely in touch with some special corner of their own working brains? Are they discovering math or creating it? And what is it like to be “sensitive” to something as abstract and ethereal as numbers?

It all makes me think a bit of physicist Max Tegmark's controversial view that all there is in the Universe is mathematics (or mathematical structure), and ultimately nothing more. But then how would such mathematical structure evolve into human brains capable of looking back on itself with objective analysis? And are the philosophers and cognitive scientists who tackle such questions simply caught in some sort of infinite regress or word loop... explaining an explanation by an explanation of an explanation of... (that really explains nothing!).
Anyway, go read about the "package delivery worker" Jianchun who, after 8 years of emailing prominent mathematicians "to no avail," finally got someone to take note.


Sunday, July 17, 2016

Of Politics and Science


"...there is a fundamental difference between science and politics. In fact, I've come to view them more and more as opposites.
"In science, progress is possible. In fact, if one believes in Bayes' theorem, scientific progress is inevitable as predictions are made and as beliefs are tested and refined. The march toward scientific progress is not always straightforward, and some well-regarded (even 'consensus') theories are later proved wrong -- but either way science tends to move toward the truth.
"In politics, by contrast, we seem to be growing ever further away from consensus. The amount of polarization between the two parties in the United States House, which had narrowed from the New Deal through the 1970s, had grown by 2011 to be the worst that it had been in at least a century."

-- Nate Silver (from "The Signal and the Noise")

Tuesday, July 12, 2016

Sunday, July 10, 2016

Uplifting...


For today's Sunday reflection, an interview interchange between Jerry Seinfeld and Judd Apatow from Apatow's book, "Sick In The Head" (no math, but somehow it appealed to me ;-):
JerryI used to keep pictures of the Hubble [Telescope] on the wall of the writing room at Seinfeld. It would calm me down when I would start to think that what I was doing was important.

JuddSee, I go the other way with that. That makes me depressed.

Jerry:  Most people would say that. People always say it makes them feel insignificant, but I don't find being insignificant depressing. I find it uplifting.

Thursday, July 7, 2016

Memories... (and Sparks)


I've occasionally thought about asking here about people's earliest memories of being attracted to mathematics. What problem/puzzle, parent/teacher, or book or event, do you remember spurring an early interest in numbers/math? 
A tweet yesterday inspires me to finally try the question out. 
"15yo has an interesting question this morning: What's the first major news story you can remember living through as a child?"
...and got a huge response from folks bringing forth early historical memories from their lives. Of course I don't expect such an outpouring for math memories, but still might be interesting.

One of my own early memories, which I've written about here before, was viewing a large, glass-encased "Galton board" at the Field Museum in Chicago (1950s), and being mesmerized, as a child, by the individual balls falling "randomly" or unpredictably from the top, yet attaining a specific pattern (Bell Curve) time and time again once all balls had settled at the bottom. Didn't really know what it meant, but knew it was something deep.

What early memories do others have that helped spark your journey to mathematics???



Wednesday, July 6, 2016

When Will I Ever Use This...


Well, in the event you become a space scientist/engineer you might just use math to embark a man-made spacecraft on a journey to a world far, far away....

No explicit mathematics today, but just thought these videos from NASA's Jet Propulsion Laboratory ought be shared, if you missed them.  First, is the jubilation of workers upon spacecraft Juno attaining orbit around Jupiter after its momentous 5-year voyage. Followed by a little more background info on the project in the second video. Amazing!:





How petty and irrelevant our localized politics and day-to-day affairs seem when shown what some humans are actually capable of accomplishing!




Sunday, July 3, 2016

An Incidental Remark...


Sunday reflection:

"In [his 1859 paper], Riemann made an incidental remark -- a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years...

"...it is that incidental remark -- the Riemann Hypothesis -- that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant at work -- subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age...

"It has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. ...Hunting down the solution to the Riemann Hypothesis has become an obsession for many -- the veritable 'great white whale' of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution."
  

-- John Derbyshire, from the dustjacket description of Prime Obsession 



==> p.s... check out my new interview with science/math writer Brian Hayes over at MathTango:
https://mathtango.blogspot.com/2016/07/brian-hayes-award-winning-science-writer.html